Venting for Half Bath

I dont do this stuff on my jobs, but this is for my house so Im going to try to tackle it myself. Mostly out of my element here.

Anyway, going to add a half bath off the kitchen directly above. Ive got a nice drain stack already. Toilet will practically be directly above. You can see in the pic the drain entering from the washer. Upper pipe is a 1 1/2″ vent that heads 20′ feet or so to the main stack.

Plan is to put a vent loop in the wall and come back down. Is this existing vent adequate to tie into? If so, what’s the proper configuration?